Problem: Simplify the expression. $(4n+1)(5n+1)$
Answer: First distribute the ${4n+1}$ onto the ${5n}$ and ${1}$ $ = {5n}({4n+1}) + {1}({4n+1})$ Then distribute the ${5n}.$ $ = ({5n} \times {4n}) + ({5n} \times {1}) + {1}({4n+1})$ $ = 20n^{2} + 5n + {1}({4n+1})$ Then distribute the ${1}$ $ = 20n^{2} + 5n + ({1} \times {4n}) + ({1} \times {1})$ $ = 20n^{2} + 5n + 4n + 1$ Finally, combine the $x$ terms. $ = 20n^{2} + 9n + 1$